{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# python绘制各种摆线（包括心形线星形线等，超炫酷）\n",
    "https://blog.csdn.net/m0_37816922/article/details/120683674?spm=1001.2014.3001.5501"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter ffmpeg unavailable; using Pillow instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from os import cpu_count\n",
    "import numpy as np\n",
    "from numpy.random import rand\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "r = 1\n",
    "theta = np.arange(0,6.4,0.1)\n",
    "xCircle0 = np.cos(theta)\n",
    "yCircle0 = 1+np.sin(theta)\n",
    "\n",
    "fig = plt.figure(figsize=(15,4))\n",
    "ax = fig.add_subplot(autoscale_on=False, \n",
    "    xlim=(1,10),ylim=(0,2))\n",
    "ax.grid()\n",
    "\n",
    "circle, = ax.plot(xCircle0,yCircle0,'-',lw=1)\n",
    "point, = ax.plot([1],[1],'o')\n",
    "trace, = ax.plot([],[],'-', lw=1)\n",
    "theta_text = ax.text(0.02,0.85,'',transform=ax.transAxes)\n",
    "textTemplate = '''x = %.1f°\\n'''\n",
    "xs,ys = [], []\n",
    "\n",
    "def animate(x):\n",
    "    if(x==0):\n",
    "        xs.clear()\n",
    "        ys.clear()\n",
    "    xCycloid = x + r*np.cos(-x) #由于是向右顺时针滚，所以角度为负\n",
    "    yCycloid = 1 + r*np.sin(-x)\n",
    "\n",
    "    xCircle = xCircle0+x\n",
    "    xs.append(xCycloid)\n",
    "    ys.append(yCycloid)\n",
    "    circle.set_data(xCircle,yCircle0)\n",
    "    point.set_data([xCycloid],[yCycloid])\n",
    "    trace.set_data(xs,ys)\n",
    "    theta_text.set_text(textTemplate % x)\n",
    "    return circle, point, trace, theta_text\n",
    "\n",
    "frames = np.arange(0,10,0.02)\n",
    "ani = animation.FuncAnimation(fig, animate, frames, \n",
    "    interval=5, blit=True)\n",
    "ani.save(\"Cycloid.gif\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter ffmpeg unavailable; using Pillow instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 1\n",
    "rIn = 0.5\n",
    "theta = np.arange(0,6.4,0.1)\n",
    "\n",
    "xCircle0 = np.cos(theta)\n",
    "yCircle0 = 1+np.sin(theta)\n",
    "xCircleOut0 = rIn*np.cos(theta)\n",
    "yCircleOut0 = 1+rIn*np.sin(theta)\n",
    "\n",
    "fig = plt.figure(figsize=(20,3))\n",
    "ax = fig.add_subplot(autoscale_on=False, \n",
    "    xlim=(1,15),ylim=(0,2))\n",
    "ax.grid()\n",
    "\n",
    "circle, = ax.plot(xCircle0,yCircle0,'-',lw=1)\n",
    "circleOut, = ax.plot(xCircleOut0,yCircleOut0,linestyle='--',lw=1)\n",
    "point, = ax.plot([1],[1],'o')\n",
    "pointOut, = ax.plot([1],[1.5],'o')\n",
    "trace, = ax.plot([],[],'-', lw=1)\n",
    "theta_text = ax.text(0.02,0.85,'',transform=ax.transAxes)\n",
    "textTemplate = '''x = %.1f\\n'''\n",
    "xs,ys = [], []\n",
    "\n",
    "def animate(x):\n",
    "    if(x==0):\n",
    "        xs.clear()\n",
    "        ys.clear()\n",
    "    xCycloid = x + r*np.cos(-x)\n",
    "    yCycloid = 1 + r*np.sin(-x)\n",
    "    xCycloidOut = x + rIn*np.cos(-x)\n",
    "    yCycloidOut = 1 + rIn*np.sin(-x)\n",
    "\n",
    "    xs.append(xCycloidOut)\n",
    "    ys.append(yCycloidOut)\n",
    "    circle.set_data(xCircle0+x,yCircle0)\n",
    "    circleOut.set_data(xCircleOut0+x,yCircleOut0)\n",
    "    point.set_data([xCycloid],[yCycloid])\n",
    "    pointOut.set_data([xCycloidOut],[yCycloidOut])\n",
    "    trace.set_data(xs,ys)\n",
    "    theta_text.set_text(textTemplate % x)\n",
    "    return circle, circleOut, point, pointOut, trace, theta_text\n",
    "\n",
    "frames = np.arange(0,15,0.1)\n",
    "ani = animation.FuncAnimation(fig, animate, frames, \n",
    "    interval=50, blit=True)\n",
    "ani.save(\"Cycloid-1.gif\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.animation:MovieWriter ffmpeg unavailable; using Pillow instead.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1\n",
    "b = 1\n",
    "theta = np.arange(0,6.4,0.05)\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(autoscale_on=False, \n",
    "    xlim=(-3,3),ylim=(-3,3))\n",
    "theta_text = ax.text(0.02,0.85,'',transform=ax.transAxes)\n",
    "textTemplate = '''θ = %.1f°\\n'''\n",
    "\n",
    "ax.grid()\n",
    "xCircle,yCircle = np.cos(theta),np.sin(theta)\n",
    "ax.plot(a*xCircle,a*yCircle,'-',lw=1)\n",
    "pt, = ax.plot([a+b],[0],'*')\n",
    "cir, = ax.plot(a+b+b*yCircle,b*yCircle,'-',lw=1)\n",
    "cycloid, = ax.plot([], [], '-', lw=1)\n",
    "\n",
    "xs,ys = [],[]\n",
    "def animate(t):\n",
    "    if(t==0):\n",
    "        xs.clear()\n",
    "        ys.clear()\n",
    "    \n",
    "    cenX = (a+b)*np.cos(t)\n",
    "    cenY = (a+b)*np.sin(t)\n",
    "    cir.set_data(cenX+b*xCircle,cenY+b*yCircle)\n",
    "    newX = cenX - b*np.cos((a+b)/b*t)\n",
    "    newY = cenY - b*np.sin((a+b)/b*t)\n",
    "    xs.append(newX)\n",
    "    ys.append(newY)\n",
    "    pt.set_data([newX],[newY])\n",
    "    cycloid.set_data(xs,ys)\n",
    "    theta_text.set_text(textTemplate % t)\n",
    "    return cycloid, cir, pt, theta_text\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, theta, \n",
    "    interval=50, blit=True)\n",
    "ani.save(\"Cycloid-2.gif\")\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:matplotlib.animation:MovieWriter ffmpeg unavailable; using Pillow instead.\n"
     ]
    }
   ],
   "source": [
    "#test.py\n",
    "#使用方法 python test.py -2 2\n",
    "# 才此环境下运行需要初始值，否则出错哦\n",
    "\n",
    "import argparse     #用于命令行的交互\n",
    "from os import cpu_count\n",
    "import numpy as np\n",
    "from numpy.random import rand\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "# 此段用于命令行赋予参数bStart 和 bEnd 的值 \n",
    "# parser = argparse.ArgumentParser()\n",
    "# parser.add_argument('bStart', type=float)\n",
    "# parser.add_argument('bEnd', type=float)\n",
    "# args = parser.parse_args()\n",
    "\n",
    "a = 1\n",
    "\n",
    "# bStart = args.bStart\n",
    "# bEnd = args.bEnd\n",
    "\n",
    "bStart = -2\n",
    "bEnd = 3\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(autoscale_on=False, \n",
    "    xlim=(-(a+2*bEnd),(a+2*bEnd)),ylim=(-(a+2*bEnd),(a+2*bEnd)))\n",
    "theta_text = ax.text(0.02,0.85,'',transform=ax.transAxes)\n",
    "textTemplate = '''a=1, b= %.2f\\n'''\n",
    "\n",
    "ax.grid()\n",
    "t = np.arange(0,6.4,0.05)\n",
    "ax.plot(a*np.cos(t),a*np.sin(t),'-',lw=1)\n",
    "cycloid, = ax.plot([], [], '-', lw=1)\n",
    "\n",
    "xs,ys = [],[]\n",
    "t = np.arange(0,30,0.05)\n",
    "\n",
    "def animate(b):    \n",
    "    xs = (a+b)*np.cos(t) - b*np.cos((a+b)/b*t)\n",
    "    ys = (a+b)*np.sin(t) - b*np.sin((a+b)/b*t)\n",
    "    cycloid.set_data(xs,ys)\n",
    "    theta_text.set_text(textTemplate % b)\n",
    "    return cycloid, theta_text\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, np.arange(bEnd,bStart,-0.02), \n",
    "    interval=50, blit=True)\n",
    "\n",
    "plt.show()\n",
    "ani.save(\"Cycloid-4.gif\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
